I am new to LiveCode so have been through quite a learning process but have enjoyed it thoroughly.
I've used LiveCode-7 on my Fedora-20 x86_64 desktop to create a LiveCode Linux application. The application that I created runs perfectly fine on my own Fedora-20 system but it refuses to run on a CentOS-6.5 platform. I've tried both 32-bit and 64-bit versions of my application on both 32-bit and 64-bit versions of CentOS-6.5 but the results are the same.

The standard advice is to check dependencies with ldd and by trying to start the application from the command line. ldd may tell you if there are version mismatches for dependencies and trying to run from the command line might tell you of those and other issues.